Analysis of the Viscous Laminar Flow in the Straight Pipe Based on the Complex Variable Finite Difference Method

Ri, Song-Chol; Jo, InGu; Pak, Namsu

doi:10.30511/ttmp.2026.2081057.1069

Analysis of the Viscous Laminar Flow in the Straight Pipe Based on the Complex Variable Finite Difference Method

Document Type : Original Article

Authors

Song-Chol Ri

InGu Jo

Namsu Pak

Faculty of Aerospace Engineering, Kim Chaek University of Technology, Pyongyang, Democratic People’s Republic of Korea

10.30511/ttmp.2026.2081057.1069

Abstract

The paper describes an efficient complex variable finite difference method (CVFDM) for calculating the two-dimensional potential flow, the viscous laminar flow in the straight pipe. The theoretical development is based on the generalization of the Cauchy-Riemann differential equation into the finite difference equation in terms of a complex variable to solve a two-dimensional boundary value problem. A numerical code is developed by this method and analytical solutions are obtained for illustrative problems. The validation of this method is confirm through the analytical solutions for Poiseuille flow and Couette flow.

Keywords

Complex Variable Finite Difference Method

Cauchy-Riemann equation

Poiseuille flow

Couette flow

Subjects